When you have sparse or limited point data, spread across a larger area of interest, and need to fill the whole area with a smooth, regular grid of predicted values, based statistically on the known point samples.

Geology, CO2 or NOx concentrations, noise... sometimes elevation.

If you have dense data, or if a result must be exact rather than statistical, then another method is usually better than Kriging. With sparse data, an exact method (such as triangulation, or gravity/inverse distance weighting) is often worse than useless, because it creates obvious artefacts.